Beating to rotational transition of a clamped active ribbon-like filament

We present a detailed study of a clamped ribbon-like filament under a compressive active force using Brownian dynamics simulations. We show that a clamped ribbon-like filament is able to capture beating as well as rotational motion under the compressive force. The nature of oscillation is governed by the torsional rigidity of the filament. The frequency of oscillation is almost independent of the torsional rigidity. The beating of the filament gives a butterfly-shaped trajectory of the free-end monomer, whereas rotational motion yields a circular trajectory on a plane. The binormal correlation and the principal component analysis reveal the butterfly, elliptical, and circular trajectories of the free end monomer. We present a phase diagram for different kinds of motion in the parameter regime of compressive force and torsional rigidity.